Question

Prove that:

(i) the parallelogram, inscribed in a circle, is a rectangle.

(ii) the rhombus, inscribed in a circle, is a square.

Answer 1

(i) Let ABCD be a parallelogram, inscribe in a circle,

(pair of opposite angles in a cyclic quadrilateral are supplementary)

the other two angles are 90° and opposite pair of sides Are equal.

∴ ABCD is a rectangle.

(pair of opposite angles in a cyclic quadrilateral are supplementary)